P-release kinetic as a predictor for P-availability in the STYCS Trials
In my Internship I studied the current GRUD, particularly Mg, P and K
Fertilizer requirement models imply \(Y\sim STP + Clay\) & \(P-\text{Export}\sim STP + Clay\)
Currently only stationary measurement of STP are considered
Could a kinetic desorption-model better explain the soil status and yield data?
The net-desorption was modeled using a first-order kinetic equation:
1. The Rate of Release: The change in P over time is proportional to the remaining desorbable P. \[\frac{dP}{dt}=k \times (P^S-P)\]
2. The Solution: When solved, this gives us the equation for the curve: \[P(t)=P^S \times (1-e^{-kt})\]
Our Goal: To find the best model for our kinetic data. First, here are the raw data points from the experiment.
We first tested the original, linearized method from the 1980s. As you can see from the dashed lines, the predictions provide a very poor fit to the actual data.
Because the old method failed, we adopted a modern non-linear approach. The solid lines show our final model, which accurately captures the desorption process. This gave us high confidence in our derived \(k\) and \(PS\) parameters.
Relevant Variables
Soil Variables:
Yield Variables:
The following random structure was chosen:
(1|year) + (1|Site) + (1|Site:block) + (Treatment|Site)
| Predictor | PS | k | log(k*PS) | CO2 | AAE10 |
|---|---|---|---|---|---|
| (Intercept) | -1.772 | -0.425 | 0.039 | -0.536 | -0.532 |
| Alox | -0.660 | -1.204 | -0.034 | -0.319 | |
| Feox | 0.020 | -0.571 | -0.164 | -0.138 | |
| soil_0_20_clay | 1.798 | -1.733** | 0.611 | -0.007 | -0.121 |
| soil_0_20_Corg | 1.044** | -0.412 | 0.166 | 0.232 | |
| soil_0_20_pH_H2O | 0.000 | -0.280 | 0.094 | 0.075 | 0.057 |
| soil_0_20_silt | 0.252 | 0.113 | -0.084 | 0.012 | |
| R2m | 1.000 | 0.204 | 0.224 | 0.125 | 0.280 |
| R2c | 1.000 | 0.963 | 0.976 | 0.724 | 0.832 |
Observation
| Predictor | Yn-STP-CO2 | Yn-STP-AAE10 | Yn-STP-GRUD | Yn-Kinetic | Yr-STP-CO2 | Yr-STP-AAE10 | Yr-STP-GRUD | Yr-Kinetic |
|---|---|---|---|---|---|---|---|---|
| (Intercept) | 0.012 | 0.007 | -0.109 | 0.156 | -0.323 | -0.257 | -0.306 | -0.119 |
| k | 0.166 | -0.018 | ||||||
| k:log(PS) | -0.012 | 0.016 | ||||||
| log(PS) | 0.066 | 0.010 | ||||||
| log(soil_0_20_P_AAE10) | 0.067* | 0.432** | 0.037 | 0.046 | ||||
| log(soil_0_20_P_CO2) | 0.027 | -0.128 | -0.001 | -0.040 | ||||
| log(soil_0_20_P_CO2):log(soil_0_20_P_AAE10) | 0.149* | -0.021 | ||||||
| R2m | 0.012 | 0.084 | 0.291 | 0.019 | 0.000 | 0.011 | 0.020 | 0.002 |
| R2c | 0.083 | 0.361 | 0.436 | 0.045 | 0.618 | 0.698 | 0.696 | 0.807 |
Observation
| Predictor | CO2_Pexport | AAE10_Pexport | Grud_Pexport | Kin_Pexport |
|---|---|---|---|---|
| (Intercept) | 0.012 | -0.002 | 0.119 | 0.596 |
| k | -0.014 | |||
| k:log(PS) | 0.080 | |||
| log(PS) | -0.018 | |||
| log(soil_0_20_P_AAE10) | 0.025 | -0.015 | ||
| log(soil_0_20_P_CO2) | 0.087 | 0.131 | ||
| log(soil_0_20_P_CO2):log(soil_0_20_P_AAE10) | 0.011 | |||
| R2m | 0.012 | 0.001 | 0.016 | 0.004 |
| R2c | 0.654 | 0.685 | 0.796 | 0.789 |
Observations
| Predictor | CO2_Pbalance | AAE10_Pbalance | Grud_Pbalance | Kin_Pbalance |
|---|---|---|---|---|
| (Intercept) | 0.569* | 0.315 | 0.610* | 1.086* |
| k | 0.155 | |||
| k:log(PS) | -0.151 | |||
| log(PS) | 0.341*** | |||
| log(soil_0_20_P_AAE10) | 0.009 | 0.009 | ||
| log(soil_0_20_P_CO2) | -0.023 | -0.029 | ||
| log(soil_0_20_P_CO2):log(soil_0_20_P_AAE10) | 0.030 | |||
| R2m | 0.001 | 0.000 | 0.006 | 0.122 |
| R2c | 0.590 | 0.762 | 0.596 | 0.699 |
Observation
Thank you for your attention